American Sign Language: "turn"

The right sign for "turn" is going to depend on your meaning.

If you mean "turn" as in "it is the next person's turn," "second hand,"
"used car," "alternate plan," and "step-brother" then use an "L"-handshape
and twist it toward the outside (or toward the person who's turn it is).
If you mean, "It is my turn," then twist it toward yourself and have it end
on your chest.

"My Turn"
Roll an "L" hand back toward your chest. You can actually
whack it up against your chest if you are adamant about it being
your turn. (Or if you just like whacking your chest.) (No comment.)

"Your turn"
Roll an "L" hand forward the person to whom you are signing. (Do NOT
whack them in the chest. If you do, I don't know you. Find another
teacher.)

"Take turns" (You and I
go back and forth)

If you mean "turn" as in turn on a computer by pushing a button then just
mime pushing a button with your thumb. Or spell "on" using a somewhat
large movement.

TURN-ON via push-button switch:
The sign above would be used for old upright "desktop" style computers. You
should modify the angle and movement to match wherever the "on button" is on
your computer or device. Note: Even though most ASL teachers avoid
using the "ON"-preposition sign, it is fairly
common for Deaf people to use the "on top of"-(preposition) sign to mean
"on" as in turn "on" your computer.

Suppose you mean "turn" as in "turn on the the lights by flipping a switch."
In that case just mime flipping a light switch upward.

TURN-ON via switch:

If you mean "turn" as in turn off a light by flipping a switch downward then
use a downward movement to mime the action.

TURN-OFF via switch:

NOTES:

There are dozens and dozens of English phrases that involve the word
"turn." Each of those phrases should be signed using an appropriate
and specific set of signs.
Concepts such as "turn the car left," "she turns me on," "it turned
out alright," "the situation took a turn for the worse" and "the
Earth turns on its axis" would all be signed very differently.

The topic of "turning" could take hours to cover and someday I'd
like to do a complete lesson on how to express the concept of
"turn." Feel free to donate gobs of money so I can speed up
development of this website eh?